zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

10sin^2(x)+11sin(x)-8=0

解答

10 sin^{2} (x) + 11 sin (x) - 8 = 0

解答

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

度数

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

10 sin^{2} (x) + 11 sin (x) - 8 = 0

用替代法求解

10 sin^{2} (x) + 11 sin (x) - 8 = 0

令

: sin (x) = u

10 u^{2} + 11 u - 8 = 0

10 u^{2} + 11 u - 8 = 0 : u = \frac{1}{2}, u = - \frac{8}{5}

10 u^{2} + 11 u - 8 = 0

使用求根公式求解

10 u^{2} + 11 u - 8 = 0

二次方程求根公式:

若

a = 10, b = 11, c = - 8

u_{1, 2} = \frac{- 11 \pm 1 1 ^{2} - 4 \cdot 10 ( - 8 )}{2 \cdot 10}

u_{1, 2} = \frac{- 11 \pm 1 1 ^{2} - 4 \cdot 10 ( - 8 )}{2 \cdot 10}

1 1^{2} - 4 \cdot 10 (- 8) = 21

1 1^{2} - 4 \cdot 10 (- 8)

使用法则

- (- a) = a

= 1 1^{2} + 4 \cdot 10 \cdot 8

数字相乘:

4 \cdot 10 \cdot 8 = 320

= 1 1^{2} + 320

1 1^{2} = 121

= 121 + 320

数字相加:

121 + 320 = 441

= 441

因式分解数字:

441 = 2 1^{2}

= 2 1^{2}

使用根式运算法则:

n a^{n} = a

2 1^{2} = 21

= 21

u_{1, 2} = \frac{- 11 \pm 21}{2 \cdot 10}

将解分隔开

u_{1} = \frac{- 11 + 21}{2 \cdot 10}, u_{2} = \frac{- 11 - 21}{2 \cdot 10}

u = \frac{- 11 + 21}{2 \cdot 10} : \frac{1}{2}

\frac{- 11 + 21}{2 \cdot 10}

数字相加/相减:

- 11 + 21 = 10

= \frac{10}{2 \cdot 10}

数字相乘:

2 \cdot 10 = 20

= \frac{10}{20}

约分:

10

= \frac{1}{2}

u = \frac{- 11 - 21}{2 \cdot 10} : - \frac{8}{5}

\frac{- 11 - 21}{2 \cdot 10}

数字相减:

- 11 - 21 = - 32

= \frac{- 32}{2 \cdot 10}

数字相乘:

2 \cdot 10 = 20

= \frac{- 32}{20}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{32}{20}

约分:

4

= - \frac{8}{5}

二次方程组的解是:

u = \frac{1}{2}, u = - \frac{8}{5}

u = sin (x)

代回

sin (x) = \frac{1}{2}, sin (x) = - \frac{8}{5}

sin (x) = \frac{1}{2}, sin (x) = - \frac{8}{5}

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - \frac{8}{5} :

无解

sin (x) = - \frac{8}{5}

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

作图

流行的例子

2cos^2(x)+7cos(x)-4=0

2 cos^{2} (x) + 7 cos (x) - 4 = 0

cot(2θ)=(sqrt(3))/3

cot (2 θ) = \frac{3}{3}

4sin^2(θ/2)+8cos(θ/2)-7=0,0<= θ<= 360

4 sin^{2} (\frac{θ}{2}) + 8 cos (\frac{θ}{2}) - 7 = 0, 0 \leq θ \leq 36 0^{\circ}

-cos(θ)+1=2cos(θ)+3

- cos (θ) + 1 = 2 cos (θ) + 3

cot^2(x)+cot(x)=0

cot^{2} (x) + cot (x) = 0